Asymptotic properties of Zeno solutions. (November 2018)

• Record Type: Journal Article
• Authors: Dashkovskiy, Sergey; Feketa, Petro
• Is Part Of: Nonlinear analysis. Volume 30(2018)
• Page Start: 256
• Page End: 265
• Publication Date: 2018-11
• Subjects: 34K34 -- 93C30; Hybrid dynamical system -- Zeno behavior -- Asymptotic stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2018.06.005
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper is concerned with problems related to Zeno solutions in hybrid dynamical systems. Zeno phenomenon is characterized by infinitely many impulses over a finite period of time and leads to a bounded time domain of solutions. Since an unbounded time domain for solutions is crucial for many applications, a method to prolong solutions to the hybrid dynamical system beyond its Zeno time is proposed in this paper. Moreover, we propose a way for asymptotic characterization of the prolonged solutions. We introduce a new concept of asymptotic stability with respect to a closed set for hybrid systems with Zeno solutions and provide sufficient conditions to verify it. The examples illustrate the proposed approach.